The existence and properties of topologically nontrivial electromagnetic field configurations within generalisations of ordinary linear Maxwell theory
thus remains certainly a topic of fascinating interest, to be pursued further, with its possible implications for the physics of nonlinear electrodynamics
phenomena within different contexts. Hopfion solitons find their mathematical and physical relevance in a growing number of different fields beyond
linear electromagnetism, ranging among others from condensed quantum matter physics to magnetohydrodynamics (see for instance Ref.[1]}).
Furthermore, nonlinear electrodynamics is witnessing an increased interest as possibly playing a relevant role in the dynamics of cosmological expansion
(see for example Refs.[2]}, [3]}, [4]}). ModMax theories lend themselves to some very sensitive experimental tests
of vacuum birefringence[5]}, [6]}, while quantum corrections are known to lead to nonlinear corrections to Maxwell's equations as in the
Heisenberg-Euler Lagrangian, albeit not necessarily conformally or duality invariant
ones. When coupled to a curved spacetime metric with its intrinsic nonlinear dynamics, nonlinear back reaction corrections to ordinary Maxwell
dynamics ought to be expected. Having theoretical models to help explore beyond the boundaries of present day fundamental theories always
enables to better test and understand the latter to their limits. The robustness to nonlinear deformations of hopfion-Rañada knots and other topologically
nontrivial electromagnetic configurations, even known as exact analytic solutions to some classes of nonlinear extensions of ordinary Maxwell theory,
makes them ideal beacons with which to project our gaze deeper into today's unknown territories at the frontiers.
